Structural Integrity of a Gingerbread House

As the holiday season approaches, gingerbread houses are again becoming a popular activity with my friends. After fall break, we made one that from Trader Joe's that was Halloween-themed and in the shape of a pentagonal prism (see below; very spooky).  It was really fun to put together, but when we were walking it to another friend's apartment, it sadly fell to pieces. This past weekend, we made another gingerbread house that was triangular-prism-shaped and holiday-themed. When making it, we accidentally watered down the icing sugar too much, but others kept going with the construction, and surprisingly, even without the icing, the house held together when we tried to move it, arguably better than the Halloween-themed one. In the past, I have only ever seen gingerbread houses in the traditional house shape with a rectangular base and a triangular roof, so I had no idea that they even made triangular gingerbread houses! We always say that for gingerbread houses, structural integrity is key, and the components of a structurally-sound gingerbread house can be explained using physics.

I began by drawing the free body diagrams for the two houses. I have drawn the forces of gravity (blue arrows) acting at the centers of mass (green dots) to illustrate the point, though they act along the whole length of the gingerbread slabs in reality. In addition to the gravitational forces, there is also friction (red arrows) holding the pieces together, preventing collapse. Though I have not shown them, there is also friction between the roof pieces and the front and back panels in both cases.

On the left is the Halloween-themed gingerbread house, with 4 major parts comprising its exterior. On the right is the holiday-themed gingerbread house with only two slabs making up its outer sides. By comparing these drawings and the general structures in the pictures above, it becomes apparent that there are significantly more forces acting in the Halloween-themed house than for the holiday one. Also, the forces in the Halloween-themed house are distributed vertically, making for greater gravitational potential energy being stored in the roof pieces of the house than in the holiday-themed one. Similarly, the whimsical tapered shape of the house with a smaller base also makes the house itself more unsteady, since the center of mass of the whole structure would be elevated in comparison to the holiday-themed one. As a result of these, even very basic consideration of physics could have predicted that the Halloween-themed house would be structurally unstable (but still very cute). In this way, we can learn from the lessons of this gingerbread calamity for future designs.

When imagining the most structurally stable gingerbread house, the isosceles triangular prism is the ideal shape, because it can distribute its gravitational forces along the gingerbread evenly, while keeping the its center of mass at its base, and minimizing the height of the house (reducing gravitational potential energy). Also, in terms of construction, it would be better to use thicker gingerbread compared to the thin and cracker-like gingerbread found in some kits. This change would provide better contact between the pieces to create a larger surface area for friction to act, thus, holding the house upright. (One could even go so far as to file down the ends of some pieces to create flat edges, which would also help increase surface area at these vertices.) Finally, to help with the friction and contact, a more viscous, somewhat hard-setting icing would be ideal since it would be able to fill in any cracks or gaps between the gingerbread pieces to increase the surface area experiencing friction with the gingerbread, and increase the coefficient of friction for these surfaces. With that, I hope this analysis can help you with any future gingerbread endeavors, and happy holidays!